\(y=e^{\frac{x}{10}}\)

Differentiate both sides with respect to x

\(\frac{dy}{dx}=\frac{d(e^{\frac{x}{10}})}{dx}\)

Using chain rule, we can write

\(\frac{dy}{dx}=\frac{d(e^{\frac{x}{10}})}{d(\frac{x}{10})}\cdot\frac{d(\frac{x}{10})}{dx}\)

Recall: \(\frac{d(e^u)}{du}=e^u\)

\(\frac{dy}{dx}=e^{\frac{x}{10}}\cdot\frac{1}{10}\)

\(\frac{dy}{dx}=\frac{e^{\frac{x}{10}}}{10}\)

Multiply both sides by dx

\(dy=\frac{e^{\frac{x}{10}}}{10dx}\)

Result: \(dy=\frac{e^{\frac{x}{10}}}{10dx}\)

Differentiate both sides with respect to x

\(\frac{dy}{dx}=\frac{d(e^{\frac{x}{10}})}{dx}\)

Using chain rule, we can write

\(\frac{dy}{dx}=\frac{d(e^{\frac{x}{10}})}{d(\frac{x}{10})}\cdot\frac{d(\frac{x}{10})}{dx}\)

Recall: \(\frac{d(e^u)}{du}=e^u\)

\(\frac{dy}{dx}=e^{\frac{x}{10}}\cdot\frac{1}{10}\)

\(\frac{dy}{dx}=\frac{e^{\frac{x}{10}}}{10}\)

Multiply both sides by dx

\(dy=\frac{e^{\frac{x}{10}}}{10dx}\)

Result: \(dy=\frac{e^{\frac{x}{10}}}{10dx}\)